An optimal expected-time parallel algorithm for Voronoi diagrams

  • Christos Levcopoulos
  • Jyrki Katajainen
  • Andrzej Lingas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 318)


We present a parallel algorithm which constructs the Voronoi diagram of a planar n-point set within a square window. When the points are independently drawn from a uniform distribution, the algorithm runs in O(log n) expected time on CRCW PRAM with O(n/log n) processors. The fast operation of the algorithm results from the efficiency of a new multi-level bucketing technique convenient in processor assignment. The concurrent write is used only for the distribution of points in their home buckets in the bottom level.


Voronoi diagram bucket method cell technique computational geometry parallel algorithms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Christos Levcopoulos
    • 1
  • Jyrki Katajainen
    • 2
  • Andrzej Lingas
    • 1
  1. 1.Department of Computer and Information ScienceLinköping UniversityLinköpingSweden
  2. 2.Department of Computer ScienceUniversity of TurkuTurkuFinland

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